Simplify to lowest terms. $\dfrac{117}{78}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 117 and 78? $117 = 3\cdot3\cdot13$ $78 = 2\cdot3\cdot13$ $\mbox{GCD}(117, 78) = 3\cdot13 = 39$ $\dfrac{117}{78} = \dfrac{3 \cdot 39}{ 2\cdot 39}$ $\hphantom{\dfrac{117}{78}} = \dfrac{3}{2} \cdot \dfrac{39}{39}$ $\hphantom{\dfrac{117}{78}} = \dfrac{3}{2} \cdot 1$ $\hphantom{\dfrac{117}{78}} = \dfrac{3}{2}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{117}{78}= \dfrac{3\cdot39}{3\cdot26}= \dfrac{3\cdot 13\cdot3}{3\cdot 13\cdot2}= \dfrac{3}{2}$